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An alternative method for distance evaluation from NOESY spectra
JOURNAL
OF MAGNETIC
76, 331-336 (1988)
RESONANCE
An Alternative Method for Distance Evaluation from NOESY Spectra GENNARO
ESPOSITO*
PAs-roREt
AND ANNALISA
*Eniricerche spa, via E. Ramarini 3240015 Monterotondo, Rome, Italy and TDepartment of Biochemistry, University of Oxford, South Parks Road, OMord, United Kingdom Received April 13, 1987; rewised July 20, 1987
.4 variety of procedures have been suggested for the quantitative analysis of 2D NOESY experiments (l-7), ranging from the simple correlation of the cross-peak heights with the internuclear distance (3) to complete relaxation matrix calculations using the experimental cross-peak and diagonal volumes (7). In this note we discuss an alternative approach first suggested by Bodenhausen and Ernst (8) and recently independently applied by Macura et al. (9) and Esposito et al. (IO), which uses the ratio between the cross peak and the diagonal peak and is independent of the initial rate approximation and any calibration. For the dipolar interaction between two nuclei A and B, the cross- and the diagonalpeak integrated intensities are described as a function of the mixing time (tm): tzAB(tm)
= -(nB/IV)MO(RAB/Rc)eXP(-RLtm)[
%&m)
= h/2N)MoexP(-RLtm)
1 - exk&hdl &A I-
- RBB R c
I+ R”;RBB)exp(-Rctm)],
where the symbols have the meaning described in Ref. (II). If a pairwise interaction between two like spins with I = 1 is assumed, the ratio of the cross-peak to diagonal intensities is equal to the ratio of the mixing coefficients: -11 - exd-&&dl @&/~RAB)
- @AA
- RBB)/~RABI
+ tVWWud
+ @AA
- RBd/2RABleXP(-&d>
’
111 where the term RL containing the leakage relaxation rates cancels out. Based on equal ;;;;~relaxation rates (i.e., RIA = RIB), R, = 21RaI and Ru = RBB, Es. [l] takes aAB/aAA
= -[
1 - exd-&&)l/[
I+
PI
exd-&dl.
In the spin diffision limit, negative NOE effects lead to the same phases for diagonal and cross peaks and the sign of the right-hand term in Eq. [2] is reversed. Rearrangement of Eq. [2] leads to
R, = WdlnK 1+ M 1- 41 331
k=l
c&r,> 1
k=-1
WC< 1,
I31
0022-2364188 $3.00 CoP&ht 0 1988 by Academic Press, Inc. AI1 Iights Of repraluaion io any form r*IQvcd.
332
NOTES
where x represents the experimental ratio between the cross and diagonal intensities. & can be expressed as R, = 21qr6[6J(2w) -J(O)]1
with
J(nw) = TJ[ 1+ (nCW$] and
q= 0.1y4h*(pf)/47r)2,
where rC and r indicate the correlation time and the internuclear distance, respectively, and the physical constants have their usual meaning. Thus r = { (2q[6J(2w) - J(O)]i/R,} “6 in which R, is given by Eq. [3]. In order to apply this method knowledge of rC is necessary. It can either be obtained from an independent determination or be calculated by rearranging Eq. [4], exploiting the known distance of a pair likely to reflect the correlation time of the whole molecule. This method should be directly compared with the approximate approaches that assume the initial rate approximation, where buildup slopes of cross-peak amplitudes (I) (or even single cross-peak heights corrected by the appropriate multiplicity factor (3)) are used. These approaches have two main drawbacks: the time-consuming collection of a series of NOESY experiments is necessary in order to select the linear region and, in using the ratio between buildup slopes or single heights of the unknown and reference pairs (12), the same leakage relaxation rates, RL, are assumed for both the reference and the unknown pairs. Different reference pairs may be needed for different RL values, a situation occurring, for instance, in the presence of selective paramagnetic perturbations or chemical-exchange contribution to the relaxation. Neither such calibration nor the initial-rate approximation are needed for the diagonal/cross-peak intensity-ratio method, where a single experiment is sufficient, performed at reasonably short values oft,,, when spin-diffusion effects are expected. As an example, we show here the results for two well-characterized peptides: gramicidin S (13, 24) (Fig. 1) and the membrane peptide alamethicin (10, 15) (Fig. 2). Table 1 lists the distances obtained for gramicidin S using Eq. [4]. Five sets of data collected at different tm were analyzed. As a comparison, the corresponding distance values from 1D NOE experiments (13) and the computed structure are also given (14). The model distances agree with the X-ray structure of the molecule (16). Very good agreement is found between the different sets of data (for uncoupled nuclei the maximum deviation is 0.2 A). The correlation time of 0.96 ns used in the calculation was computed from Eq. [4] using the known distance (1.77 A) between the two geminal 6 protons of proline. This value agrees, within the experimental error, with an independent determination obtained for the same pair from the ratio of their T, values measured at 500 and 300 MHz (0.83 ns). The T, frequency-dependence measurements were carried out to check the reliability of the correlation time obtained from NOESY data, rather than to estimate it accurately. As expected, the unavoidable effect of spin diffusion leads to an underestimation of rC, even for nuclei whose relaxation is dominated by the strong geminal dipolar interaction, such as the 6 protons of proline. Minor discrepancies between some of the NH to H, distances compared with the corresponding H, to NH distances, measured at short mixing times, can be ascribed partially to an imperfect suppression of the zero-quantum contribution arising from
333
NOTES
‘pm
41)
45
50
FIG. 1. ‘H 500 MHz 2D pure-phase NOESY spectrum of 40 m&f gramicidin S (cyclo(Pro-Val-OmLeu-r+Phe)2) in DMSO-d6 (T = 303 + 1 K). NH-&H connectivities (assignment according to Ref. (13). Thirty-two scans were collected with a sweep width of 5000 Hz in both dimensions on a Bruker AM-500 spectrometer. Quadrature detection in t, domain was achieved by the TPPI method. The original data matrix was 5 12 X 4 K and was zero-filled once in 1,. No ftlter was applied prior to Fourier transformation. Five different values of mixing time were used (80, 100, 150, 350, and 600 ms). A random variation oft, was also allowed to suppress coherent contributions arising from scalar coupling. Integrals were evaluated from cross sections along t2.
the scalar coupling and partially to baseline distortions. With the exception of the GPro-arPhe distance at t,,, = 600 ms, where the distance is presumably affected by spindiffusion and multispin effects, no significant deviations are found even at quite long tm. It is also worth noting that multispin effects present limited consequences, even in situations where one would expect considerable effects (7, 17). In the case of GPro protons, which are 1.77 A apart, both nuclei are also close to PheaCH (2.21 and 2.24 A). The pairwise interaction approximation works satisfactorily in this case, the largest deviation being less than 0.2 A for t, =S350 ms. Table 2 lists the NOE connectivities for some of the NH protons in alamethicin, again using Eq. [4]. In methanol, alamethicin has been shown to adopt a helical
334
NOTES
FIG. 2. NH-NH connectivities from a ‘H 500 MHz pure-phase NOISY spectrum of 6 mM alamethicin in CDsOH at pH* 6.1. The primary structure of afamethicin is acetyl-Aib-Pro-Aib-Ala-Aib-Ala-CmAib-VaL4ib-Gly-Leu-Aib-Pro-Val-Aib-Aib-Glu-Gln-Phol (JO). The network of consecutive NH-NH NOES (those missing in the figure are seen at higher contour levels) and the values of JNHnindicate that the molecule adopts a helical structure in solution. Sixty-four scans were collected with a sweep width of +2400 Hz in both dimensions on a home-built 500 MHz spectrometer with a Nicolet/GE 1280 computer. The solvent OH resonance was suppressed by selective irradiation during the recycling time and the mixing time. Quadrature detection in 1, was accomplished using the States method: two 5 12 X 4 K matrices were acquired and a double zero-filling was performed in tl in order to produce a final 2 K X 2 K real matrix. No filter was applied.
conformation similar to the crystal structure (10, IS). The correlation time (0.72 ns) was calculated using the 6Pro’ proton NOESY cross peaks. The intrinsic accuracy limits of the intensity measurements are rather severe for cross peaks exhibiting intensities in the range I-34 of the diagonal. In addition, the accuracy of the correlation time is quite critical in a region where the approximation & = 2 W, does not strictly hold (~7, = 2.3) (II). Nevertheless, the small distances calculated from a set of sequential NH-NH NOESY connectivities were around the typical value for helices (2.7 A) (IS). The method discussed here is simple and time saving, yet still accurate enough for most practical purposes. Its main limitation arises from the possible overlap of diagonal peaks, which is most likely to occur in large molecules. For small molecules, a careful choice of the cross section usually allows deconvolution of most of the maxima of contiguous diagonal peaks. In our experiments, overlaps caused very few problems. Additional sources of error for the intensity ratio method arise from experimental
335
NOTES TABLE 1 Internuclear Distances (A) in Gramicidin S from 2D NOESY, ID NOE, and Energy Calculations INTRA method’ (&,,(ms)) DiagOIXil
NHPhe aLesI Nlmm &al NHL&U aom c&e
Crosspeak
80
100
150
350
600
1D methodb
Model’
c&x NHPhe
2.12 1.98 2.10 2.0, 2.00 1.9, 2.0, 1.96 2.04 2.2,
2.0, 2.2, 2.05 2.0s 1.9, 2.0, 2.16 2.1, 2.1, 2.1,
2.16 2.2, 2.12 2.0s 2.0s 2.0, 2.2, 2.1, 2.20 2.2,
2.12 2.26 2.0s 2.14 2.0, 2.12 2.32 2.13 2.30 2.09
2.06 2.2, 2.0, 2.1, 2.00 2.0s 2.2, 1.99 2.44 1.9, 3.10
2.05
2.19
2.00
2.24
2.04
2.22
2.04
2.21
2.14
2.24
2.54
3.39
2.71
2.80
2.73
2.71
2.63
2.86
2.69
2.83
CIVal
&pro
NHDrn c&m NHLeu i&Pro aPhe &Pro aPhe
NHVal
aPro
CuprO
NHVal
NHLeu
OlLeU
2.50
2.11 2.68 2.45
2.10
2.12
2.8, 2.58
&Xl
NHLeu olPhe NHPhe c&m NHOm oval NHVal
2.1s
2.6,
2.g6
2.g9
2.8,
2.4, 2.72 2.46 2.69 2.4,
2.6, 2.56
2.5, 3.14 2.7, 2.9, 3.0, 2.72
2.56 2.76 2.6,, 2.7, 2.6s 2.73
WI0
c#he
NHPhe aPhe NHOm 0Om NHVat 0rVal
2.8j, 2.2)
2.60
a This work. b Ref. (13). ‘Ref. (14).
TABLE 2 Internuclear Distances (A) in Alamcthicin from 2D NOESY and X-Ray Structure Diagonal
cross peak
Ala-4 Aib8
Aib5
val-9 Aib-10
AiblO Glyll
val9
Am-10
va19
Leu-12 Leu-12
Aibl3 Giyll Aibl7 Aib17
Aib-16 Glu-18 ’ This work. b Ref. (IS).
INTRA method”
crystal structureb
2.6 2.9 2.1 2.7 2.9 2.4 2.5 2.9 2.8
2.98 2.75 2.77 2.75 2.77 2.52 2.58 3.01 2.87
336
NOTES
uncertainty in the integral estimation and in the calculation of the correlation time. Errors in the integral evaluation can be reduced by using sufficient resolution in both time dimensions and by removing possible causes of baseline distortion. For the cases examined, we estimate that a limiting error of 0.3 A on the final distance would result from a 50% inaccuracy of the intensity ratio. As shown by Clore et al. (19), the accuracy demand on T, is usually not very stringent for distance calculation purposes. ACKNOWLEDGMENTS We thank Karon Topping for the gramicidin sample and Dr. J. Boyd and Dr. I. D. Campbell for useful discussions. We also thank Eniricerche spa. and Medical Research Council for financial support. REFERENCES 1. ANIL KUMAR, G. WAGNER, R. R. ERNST, AND K. WOTHRICH, J. Am. Chem. Sot. 103,3654 (1981). 2. H. KESSLER, W. BERIUEL, A. FRIEDRICH, G. KRACK, AND W. E. HULL, .I. Am. Chem. Sot. 104,6297 (1982). 3. M. P. WILLIAMSON, T. F. HAVEL, AND K. WUTHRICH, .I Mol. Biol. 182,295 (1985). 4. J. W. KEEPERS AND T. L. JAMES, J. Magn. Reson. 57,404 (1984). 5. W. MASSEFSKI AND P. H. BOLTON, J. Magn. Reson. 65,526 (1985). 6. E. R. JOHNSTON, M. J. DELLWO, AND J. HENDRIX, J. Mum. Reson. 66,399 (1986). 7. E. T. OLEJNICZAK, R. T. GAMPE, AND S. W. FESIK, .I Magn. Reson. 67,28 (I 986). 8. G. B~DENHALJSEN AND R. R. ERNST, J. Am. Chem. Sot. 104, 1304 (1982). 9. S. MACURA, B. T. FARMER, AND L. R. BROWN, J. Mugn. Reson. 70,493 (1986). 10. G. ESPOSITO, J. A. CARVER, J. Boys, AND I. D. CAMPBELL, Biochemistry 26, 1043 (1987). II. S. MACIJRA AND R. R. ERNST, Mol. Phys. 41,95 (1980). 12. W. BRAUN, C. BOESCH, L. R. BROWN, N. G0, AND K. WUTHRICH, Biochem. Biophys. Acta 667,377
(1981). 13. C. R. JONES, C. T. SIKAKANA, S. HEHIR, M. Kuo, AND W. A. GIBBONS, Biophys. J. 24,815 (1978). 14. M. DYGERT, N. G0, AND H. A. SCHERAGA, Macromolecules 8,750 (1975). 15. R. 0. Fox AND F. M. RICHARDS, Nature (London) 300, 325 (1982). 16. S. E. HULL, R. KARLSSON, P. M&N, M. M. WOOLFSON, AND E. J. D~DSON, Nature (London) 275, 206 (1978). 17. G. M. CLORE AND A. M. GRONENBORN, J. Magn. Reson. 61, 158 (1985). 18. K. W~THRICH, M. BILLETER, AND W. BFUJN, J. Mol. Biol. 180,715 (1984). 19. G. M. CLORE, A. M. GRONENESORN, AND L. W. MCLAUGHLIN, Eur. J. Biochem. 151, 153 (1985).
OF MAGNETIC
76, 331-336 (1988)
RESONANCE
An Alternative Method for Distance Evaluation from NOESY Spectra GENNARO
ESPOSITO*
PAs-roREt
AND ANNALISA
*Eniricerche spa, via E. Ramarini 3240015 Monterotondo, Rome, Italy and TDepartment of Biochemistry, University of Oxford, South Parks Road, OMord, United Kingdom Received April 13, 1987; rewised July 20, 1987
.4 variety of procedures have been suggested for the quantitative analysis of 2D NOESY experiments (l-7), ranging from the simple correlation of the cross-peak heights with the internuclear distance (3) to complete relaxation matrix calculations using the experimental cross-peak and diagonal volumes (7). In this note we discuss an alternative approach first suggested by Bodenhausen and Ernst (8) and recently independently applied by Macura et al. (9) and Esposito et al. (IO), which uses the ratio between the cross peak and the diagonal peak and is independent of the initial rate approximation and any calibration. For the dipolar interaction between two nuclei A and B, the cross- and the diagonalpeak integrated intensities are described as a function of the mixing time (tm): tzAB(tm)
= -(nB/IV)MO(RAB/Rc)eXP(-RLtm)[
%&m)
= h/2N)MoexP(-RLtm)
1 - exk&hdl &A I-
- RBB R c
I+ R”;RBB)exp(-Rctm)],
where the symbols have the meaning described in Ref. (II). If a pairwise interaction between two like spins with I = 1 is assumed, the ratio of the cross-peak to diagonal intensities is equal to the ratio of the mixing coefficients: -11 - exd-&&dl @&/~RAB)
- @AA
- RBB)/~RABI
+ tVWWud
+ @AA
- RBd/2RABleXP(-&d>
’
111 where the term RL containing the leakage relaxation rates cancels out. Based on equal ;;;;~relaxation rates (i.e., RIA = RIB), R, = 21RaI and Ru = RBB, Es. [l] takes aAB/aAA
= -[
1 - exd-&&)l/[
I+
PI
exd-&dl.
In the spin diffision limit, negative NOE effects lead to the same phases for diagonal and cross peaks and the sign of the right-hand term in Eq. [2] is reversed. Rearrangement of Eq. [2] leads to
R, = WdlnK 1+ M 1- 41 331
k=l
c&r,> 1
k=-1
WC< 1,
I31
0022-2364188 $3.00 CoP&ht 0 1988 by Academic Press, Inc. AI1 Iights Of repraluaion io any form r*IQvcd.
332
NOTES
where x represents the experimental ratio between the cross and diagonal intensities. & can be expressed as R, = 21qr6[6J(2w) -J(O)]1
with
J(nw) = TJ[ 1+ (nCW$] and
q= 0.1y4h*(pf)/47r)2,
where rC and r indicate the correlation time and the internuclear distance, respectively, and the physical constants have their usual meaning. Thus r = { (2q[6J(2w) - J(O)]i/R,} “6 in which R, is given by Eq. [3]. In order to apply this method knowledge of rC is necessary. It can either be obtained from an independent determination or be calculated by rearranging Eq. [4], exploiting the known distance of a pair likely to reflect the correlation time of the whole molecule. This method should be directly compared with the approximate approaches that assume the initial rate approximation, where buildup slopes of cross-peak amplitudes (I) (or even single cross-peak heights corrected by the appropriate multiplicity factor (3)) are used. These approaches have two main drawbacks: the time-consuming collection of a series of NOESY experiments is necessary in order to select the linear region and, in using the ratio between buildup slopes or single heights of the unknown and reference pairs (12), the same leakage relaxation rates, RL, are assumed for both the reference and the unknown pairs. Different reference pairs may be needed for different RL values, a situation occurring, for instance, in the presence of selective paramagnetic perturbations or chemical-exchange contribution to the relaxation. Neither such calibration nor the initial-rate approximation are needed for the diagonal/cross-peak intensity-ratio method, where a single experiment is sufficient, performed at reasonably short values oft,,, when spin-diffusion effects are expected. As an example, we show here the results for two well-characterized peptides: gramicidin S (13, 24) (Fig. 1) and the membrane peptide alamethicin (10, 15) (Fig. 2). Table 1 lists the distances obtained for gramicidin S using Eq. [4]. Five sets of data collected at different tm were analyzed. As a comparison, the corresponding distance values from 1D NOE experiments (13) and the computed structure are also given (14). The model distances agree with the X-ray structure of the molecule (16). Very good agreement is found between the different sets of data (for uncoupled nuclei the maximum deviation is 0.2 A). The correlation time of 0.96 ns used in the calculation was computed from Eq. [4] using the known distance (1.77 A) between the two geminal 6 protons of proline. This value agrees, within the experimental error, with an independent determination obtained for the same pair from the ratio of their T, values measured at 500 and 300 MHz (0.83 ns). The T, frequency-dependence measurements were carried out to check the reliability of the correlation time obtained from NOESY data, rather than to estimate it accurately. As expected, the unavoidable effect of spin diffusion leads to an underestimation of rC, even for nuclei whose relaxation is dominated by the strong geminal dipolar interaction, such as the 6 protons of proline. Minor discrepancies between some of the NH to H, distances compared with the corresponding H, to NH distances, measured at short mixing times, can be ascribed partially to an imperfect suppression of the zero-quantum contribution arising from
333
NOTES
‘pm
41)
45
50
FIG. 1. ‘H 500 MHz 2D pure-phase NOESY spectrum of 40 m&f gramicidin S (cyclo(Pro-Val-OmLeu-r+Phe)2) in DMSO-d6 (T = 303 + 1 K). NH-&H connectivities (assignment according to Ref. (13). Thirty-two scans were collected with a sweep width of 5000 Hz in both dimensions on a Bruker AM-500 spectrometer. Quadrature detection in t, domain was achieved by the TPPI method. The original data matrix was 5 12 X 4 K and was zero-filled once in 1,. No ftlter was applied prior to Fourier transformation. Five different values of mixing time were used (80, 100, 150, 350, and 600 ms). A random variation oft, was also allowed to suppress coherent contributions arising from scalar coupling. Integrals were evaluated from cross sections along t2.
the scalar coupling and partially to baseline distortions. With the exception of the GPro-arPhe distance at t,,, = 600 ms, where the distance is presumably affected by spindiffusion and multispin effects, no significant deviations are found even at quite long tm. It is also worth noting that multispin effects present limited consequences, even in situations where one would expect considerable effects (7, 17). In the case of GPro protons, which are 1.77 A apart, both nuclei are also close to PheaCH (2.21 and 2.24 A). The pairwise interaction approximation works satisfactorily in this case, the largest deviation being less than 0.2 A for t, =S350 ms. Table 2 lists the NOE connectivities for some of the NH protons in alamethicin, again using Eq. [4]. In methanol, alamethicin has been shown to adopt a helical
334
NOTES
FIG. 2. NH-NH connectivities from a ‘H 500 MHz pure-phase NOISY spectrum of 6 mM alamethicin in CDsOH at pH* 6.1. The primary structure of afamethicin is acetyl-Aib-Pro-Aib-Ala-Aib-Ala-CmAib-VaL4ib-Gly-Leu-Aib-Pro-Val-Aib-Aib-Glu-Gln-Phol (JO). The network of consecutive NH-NH NOES (those missing in the figure are seen at higher contour levels) and the values of JNHnindicate that the molecule adopts a helical structure in solution. Sixty-four scans were collected with a sweep width of +2400 Hz in both dimensions on a home-built 500 MHz spectrometer with a Nicolet/GE 1280 computer. The solvent OH resonance was suppressed by selective irradiation during the recycling time and the mixing time. Quadrature detection in 1, was accomplished using the States method: two 5 12 X 4 K matrices were acquired and a double zero-filling was performed in tl in order to produce a final 2 K X 2 K real matrix. No filter was applied.
conformation similar to the crystal structure (10, IS). The correlation time (0.72 ns) was calculated using the 6Pro’ proton NOESY cross peaks. The intrinsic accuracy limits of the intensity measurements are rather severe for cross peaks exhibiting intensities in the range I-34 of the diagonal. In addition, the accuracy of the correlation time is quite critical in a region where the approximation & = 2 W, does not strictly hold (~7, = 2.3) (II). Nevertheless, the small distances calculated from a set of sequential NH-NH NOESY connectivities were around the typical value for helices (2.7 A) (IS). The method discussed here is simple and time saving, yet still accurate enough for most practical purposes. Its main limitation arises from the possible overlap of diagonal peaks, which is most likely to occur in large molecules. For small molecules, a careful choice of the cross section usually allows deconvolution of most of the maxima of contiguous diagonal peaks. In our experiments, overlaps caused very few problems. Additional sources of error for the intensity ratio method arise from experimental
335
NOTES TABLE 1 Internuclear Distances (A) in Gramicidin S from 2D NOESY, ID NOE, and Energy Calculations INTRA method’ (&,,(ms)) DiagOIXil
NHPhe aLesI Nlmm &al NHL&U aom c&e
Crosspeak
80
100
150
350
600
1D methodb
Model’
c&x NHPhe
2.12 1.98 2.10 2.0, 2.00 1.9, 2.0, 1.96 2.04 2.2,
2.0, 2.2, 2.05 2.0s 1.9, 2.0, 2.16 2.1, 2.1, 2.1,
2.16 2.2, 2.12 2.0s 2.0s 2.0, 2.2, 2.1, 2.20 2.2,
2.12 2.26 2.0s 2.14 2.0, 2.12 2.32 2.13 2.30 2.09
2.06 2.2, 2.0, 2.1, 2.00 2.0s 2.2, 1.99 2.44 1.9, 3.10
2.05
2.19
2.00
2.24
2.04
2.22
2.04
2.21
2.14
2.24
2.54
3.39
2.71
2.80
2.73
2.71
2.63
2.86
2.69
2.83
CIVal
&pro
NHDrn c&m NHLeu i&Pro aPhe &Pro aPhe
NHVal
aPro
CuprO
NHVal
NHLeu
OlLeU
2.50
2.11 2.68 2.45
2.10
2.12
2.8, 2.58
&Xl
NHLeu olPhe NHPhe c&m NHOm oval NHVal
2.1s
2.6,
2.g6
2.g9
2.8,
2.4, 2.72 2.46 2.69 2.4,
2.6, 2.56
2.5, 3.14 2.7, 2.9, 3.0, 2.72
2.56 2.76 2.6,, 2.7, 2.6s 2.73
WI0
c#he
NHPhe aPhe NHOm 0Om NHVat 0rVal
2.8j, 2.2)
2.60
a This work. b Ref. (13). ‘Ref. (14).
TABLE 2 Internuclear Distances (A) in Alamcthicin from 2D NOESY and X-Ray Structure Diagonal
cross peak
Ala-4 Aib8
Aib5
val-9 Aib-10
AiblO Glyll
val9
Am-10
va19
Leu-12 Leu-12
Aibl3 Giyll Aibl7 Aib17
Aib-16 Glu-18 ’ This work. b Ref. (IS).
INTRA method”
crystal structureb
2.6 2.9 2.1 2.7 2.9 2.4 2.5 2.9 2.8
2.98 2.75 2.77 2.75 2.77 2.52 2.58 3.01 2.87
336
NOTES
uncertainty in the integral estimation and in the calculation of the correlation time. Errors in the integral evaluation can be reduced by using sufficient resolution in both time dimensions and by removing possible causes of baseline distortion. For the cases examined, we estimate that a limiting error of 0.3 A on the final distance would result from a 50% inaccuracy of the intensity ratio. As shown by Clore et al. (19), the accuracy demand on T, is usually not very stringent for distance calculation purposes. ACKNOWLEDGMENTS We thank Karon Topping for the gramicidin sample and Dr. J. Boyd and Dr. I. D. Campbell for useful discussions. We also thank Eniricerche spa. and Medical Research Council for financial support. REFERENCES 1. ANIL KUMAR, G. WAGNER, R. R. ERNST, AND K. WOTHRICH, J. Am. Chem. Sot. 103,3654 (1981). 2. H. KESSLER, W. BERIUEL, A. FRIEDRICH, G. KRACK, AND W. E. HULL, .I. Am. Chem. Sot. 104,6297 (1982). 3. M. P. WILLIAMSON, T. F. HAVEL, AND K. WUTHRICH, .I Mol. Biol. 182,295 (1985). 4. J. W. KEEPERS AND T. L. JAMES, J. Magn. Reson. 57,404 (1984). 5. W. MASSEFSKI AND P. H. BOLTON, J. Magn. Reson. 65,526 (1985). 6. E. R. JOHNSTON, M. J. DELLWO, AND J. HENDRIX, J. Mum. Reson. 66,399 (1986). 7. E. T. OLEJNICZAK, R. T. GAMPE, AND S. W. FESIK, .I Magn. Reson. 67,28 (I 986). 8. G. B~DENHALJSEN AND R. R. ERNST, J. Am. Chem. Sot. 104, 1304 (1982). 9. S. MACURA, B. T. FARMER, AND L. R. BROWN, J. Mugn. Reson. 70,493 (1986). 10. G. ESPOSITO, J. A. CARVER, J. Boys, AND I. D. CAMPBELL, Biochemistry 26, 1043 (1987). II. S. MACIJRA AND R. R. ERNST, Mol. Phys. 41,95 (1980). 12. W. BRAUN, C. BOESCH, L. R. BROWN, N. G0, AND K. WUTHRICH, Biochem. Biophys. Acta 667,377
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